PEACH home tutor: explanation? (spoilers)

100% spoilerific questions - can't seem to make sense of the plot, although it looks like it was intended for this Hmanga to have a coherent one...

Oh, well, I guess a first-page question can't be a spoiler:

#0. Is headbutting her new student just her way of saying "Hi! Beware, random crazy woman!", or was there something lost in translation/missing pages/missing intro text/etc?

The rest I'll spoiler-tag.

Spoiler (mouse over to view)

1. OK, so we're specifically told that the peach water is important, but what's that got to do with blowjobs/sex? Is there some wordplay or symbolism lost in translation?2. Why Tuesdays/Fridays, what is the significance of that? Or is that when the manga magazines she requests come out, so it's like she's "thanking" him for lending her his manga?3. Why does she perceive having period sex for a guy's first time to be an especially twisted way to hurt him? This bloke seems rather like the go-with-the-flow (pun not intended) whatever-it's-cool type, not the kind to freak out and get traumatized by a little thing like that??3.b. ...Or was it meant that she wanted to use her period to fake having been a virgin or having been physically injured by him somehow, and somehow play with him using those avenues to pressure him?3.c. OR was it somehow meant to imply that she intentionally had period sex to hide having actually been a virgin?4. Really, why the blindfolds? Was she strongly implied to be hiding something specific, like starting out exploring at an experience level much like the guy's, but putting up a false facade of calm, in-control, and very knowledgeable? Or was that just an artificial wall to keep her own trust issues at bay by giving her full control and/or making her "invisible" in moments of maximum closeness?5. ...or is that just her kind of kink, which she's covered up with a half-assed lie about the purpose having something to do with his virginity?6. Why does she think she's a baaaaaad girl? Or is it the flirting with, charming, and giving blowjobs to her younger male student - in other words, their entire connection - that makes her bad? Or was it about getting paid for these lessons, but just having fun and/or making sexual acts a prominent part of them??7. What *was* she laughing about so hard in the very last scene?

...or was this just a pilot episode for a potential serialization that never got picked up, hence all the loose ends and very little understanding after completing the 1 chapter?

PS at the end of the volume, there's unscanlated Japanese text, handwritten, several pages thereof - which seems to contain chapter titles... are these explanations/epilogues/background plot info, or the usual "I wrote this on a rainy november, sorry about the crappy backgrounds I accidentally took the wrong train and scouted the wrong city, and then my editor rode me hard so I just handed in rough drafts"-style author excuses/filler for a couple of pages to up the count?